Theorem remulr

Description: The multiplication operation of the field of reals. (Contributed by Thierry Arnoux, 1-Nov-2017)

	Ref	Expression
Assertion	remulr	|- x. = ( .r ` RRfld )

Proof

Step	Hyp	Ref	Expression
1		reex	|- RR e. _V
2		df-refld	|- RRfld = ( CCfld |`s RR )
3		cnfldmul	|- x. = ( .r ` CCfld )
4	2 3	ressmulr	|- ( RR e. _V -> x. = ( .r ` RRfld ) )
5	1 4	ax-mp	|- x. = ( .r ` RRfld )